A 150 -lb student on a steadily rotating Ferris wheel is...

A 150 -lb student on a steadily rotating Ferris wheel is sitting on a scale that reads $125 \mathrm{lb}$ at the highest point. $(a)$ What is the scale reading at the lowest point? $(b)$ What would be the scale reading at the highest point if the speed of the Ferris wheel were doubled?

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Key Concepts

Centripetal Acceleration

Centripetal acceleration is the inward acceleration required for an object to follow a circular path. It is determined by the relationship a = v²/r, where v is the object's speed and r is the radius of the circle. This concept explains how additional forces must be present to keep an object moving in a curve and is essential in understanding how normal forces are modified in a rotating system.

Apparent Weight

Apparent weight is the reading a scale provides, which corresponds to the normal force exerted on an object rather than its actual gravitational force. In a non-accelerating situation, this is equal to the object's true weight. However, in circular motion, the need for centripetal force alters the normal force, making the apparent weight differ from the actual weight, depending on the object's position in the circle.

Dependence on Speed in Circular Motion

The requirement for centripetal force depends on the square of the speed, meaning that any changes in speed have a significant effect on the net force acting on the object. When the speed of the rotating system is doubled, the centripetal acceleration (and thus the additional force requirement) increases by a factor of four, which directly influences the scale reading or apparent weight.

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